Method for determining the short axis in a lesion region in a three dimensional medical image

ABSTRACT

A short axis in a 3 dimensional image of a lesion is determined starting from voxels defining the long axis and voxels in the plane of the long axis. Voxels within the plane of the long axis are projected perpendicularly onto the long axis and receive an identifier indicative of the region on the long axis onto which they are projected. Distances between points (projected sub-voxels) in pairs of points within the same range and within adjacent ranges are evaluated in order to determine the longest distance.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a 371 National Stage Application ofPCT/EP2015/079916, filed Dec. 16, 2015. This application claims thebenefit of priority to European Application No. 15150133.5, filed Jan.6, 2015, which is incorporated by reference herein in its entirety.

BACKGROUND OF THE INVENTION 1. Field of the Invention

The present invention relates to a method of computing an axis along apredefined direction in a 3 dimensional medical image representation.The invention more specifically relates to a method of determining theshort axis in a 3 dimensional image of a lesion, e.g. a tumor.

2. Description of the Related Art

Short and long axes are important measures to reflect the threedimensional size of lesions. These measures are used to evaluate andfollow up a lesion in medical diagnosis and treatment.

These measures are used for example in the RECIST (Response EvaluationCriteria In Solid Tumors) standard to define how a tumor responds,stabilizes or progresses during treatment.

Processed nodules are extracted from 3D reconstructions of MRI (magneticresonance imaging) or CT (X-ray computed tomography).

The short and long axes are defined in the same plane. The direction ofthis plane is predefined. It usually corresponds to the direction of thenative slices (the DICOM images). The plane itself is computed whilecomputing the long axis.

Given a pair of points (voxels) defining the long axis in a plane, alsocalled maximum diameter corresponding to the maximum distance betweenany two points in the plane, the short axis is defined as theperpendicular longest axis to the long axis.

It corresponds to the maximum distance between any two points in the setthat define a perpendicular axis to the long axis. Both axes are definedin the same plane which usually corresponds to the volume native planes(slices, DICOM images, example in FIG. 1).

A number of algorithms proposing a fast estimation of the long axisexist in the literature.

However there is still a demand for an accurate method for estimation ofthe short axis.

SUMMARY OF THE INVENTION

It is an aspect of the present invention to provide a fast and accuratemethod to compute the short axis of a set of voxels.

Further objects will become apparent from the description given below.

The above-mentioned aspects are realised by a computer-implementedmethod having the method steps set out below.

The method has been designed to operate on CT and MRI 3Dreconstructions, but can be applied to any 2D image.

The invention relates to the computation of the short axis. The longaxis can also be computed using a well-known method.

The method starts from a set of voxels defining a 3D lesion and thedirection of the plane containing the axes (usually the native slicedirection).

If the acquisition is a 2D image, the method starts from this image.

Input of the pair of voxels defining the long axis as well as itscorresponding plane can be computed within the method of the presentinvention (as described below in the detailed description).

However, the long axis can also be determined in advance. Its definitioncan be stored in and retrieved from memory or can be determined inadvance of the steps of the method for determining the short axis.

Specific features for preferred embodiments of the invention are set outbelow.

The present invention is generally implemented as a computer programproduct adapted to carry out the method of any of the claims when run ona computer and is stored on a computer readable medium.

Further advantages and embodiments of the present invention will becomeapparent from the following description and drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates the short and long axes in native planes of a 3Dvolume representation.

FIG. 2 illustrates the method of computation of the short axis accordingto the present invention applied to a 5 voxel mask.

FIG. 3 illustrates a refinement of the short axis computation method ofthe present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The short and the long axes computation requires the input of a set ofvoxels.

These voxels may correspond to all voxels contained in a lesion mask.

The lesion mask can be obtained by any lesion segmentation method, e.g.the one described in co-pending European patent application 13168875.6entitled “Method of defining a region of interest”, filed on May 23,2013.

The position of the long axis, as well as the plane in which it isdefined is required to compute the short axis according to the method ofthe present invention.

The long axis computation requires the input of a set of voxels definingthe lesion and the direction of the plane containing the axes (usuallythe native slice direction)

Several methods exist to compute the long axis. Below an example of sucha method is described.

Example of Long Axis Computation

For each plane orthogonal to the given direction, the distance betweeneach pair of points is computed (in this exemplary embodiment, thedistance from voxel center to voxel center is considered). The pair ofpoints having the maximum distance defines the local diameter in itscorresponding plane.

Among the local diameters defined for each plane, the maximum diameteris defined as the diameter with the largest of the above distances. Thisdiameter, as well as the plane where it is found, are used as input forthe short axis algorithm, e.g. as a set of voxels defining the plane onone hand and a pair of voxels defining the long axis in the other hand.

The above algorithm provides the maximum diameter defined using voxelcenters (FIG. 2 .b).

In a following step the centers can be replaced by corner values to geta more accurate diameter (FIG. 2 .c). In the illustrated embodiment‘center’ corresponds to the voxel parallelepiped geometrical center.

The algorithm can be run with the voxel centers instead of voxel cornersas input in order to have less data to process.

Short Axis Computation According to the Invention:

Let u be a unit vector collinear to the long axis and v a unit vectorperpendicular to u in the input plane.

Voxel_size is a 3D vector defining the voxel size (in mm). Max_deviationis a user defined parameter which is used to control the maximumdeviation angle allowed from v direction. To get a short axis whichmakes an angle of exactly 90° with the long axis, this parameter shouldbe set to 0°.

1. Define an initial range width called range_width such as:range_width=Voxel_size·u

This formula provides the most optimal result for the next step ofsampling/clustering, since it provides a range with the size of aprojected voxel so only aligned voxels will be in the same range.

Alternative formulae may be used but might demand a larger number ofiterations. Larger ranges may be envisaged if Max_deviation is large.

2. Sample the long axis.

The long axis is sampled by subdividing it into a set of equal sizeranges. Each range width is range_width (FIG. 2 .d). In the following,the words range, cluster and sample refer to the same reference.

3. Each point from the input set of voxels is projected along u andassigned to one of the ranges according to the position of itsprojection value (in FIG. 2 .d each range member is assigned the sameidentifier). In this way clusters of voxels assigned to the same rangeare generated.

4. Within each cluster, find internally the most distant pair of points,if any. Let intra_candidate be the pair of points having the maximumdistance among all clusters (in FIG. 2 .e, intra_candidate points arehighlighted). At this level in this embodiment, distances are computedbetween voxel centers.

Alternatively one of the voxel corners can be considered instead (mustbe the same corner), e.g. the distances can be computed between top leftcorner to top left corner.

5. Evaluate the pair intra_candidate. The evaluation algorithm isdescribed in the following section. This algorithm determines whetherthe input pair is a valid candidate and, if valid, replaces the voxelcenters by edge points.

A pair is considered a valid pair if inside the voxels of the pair anaxis can be drawn that is substantially perpendicular to the long axis,“substantially perpendicular” in the context of this invention meaningthat the deviation angle of the direction of this axis from thedirection perpendicular to the long axis is smaller than a pre-definedvalue max_deviation.

The value of the deviation angle can be set by the user.

It can be set to 0° to get accurate results. A few degrees more can beacceptable (e.g. 5° is a good compromise according to experiments).

6. For each range range_i, find the pair of points (if any) defining themaximum distance such that one point belongs to range_i and the otherpoint belongs to an adjacent range to range_i. If a pair of points infound for range_i, it is added to a list of pairs calledinter_candidantes. At this level, distances are also computed usingvoxel centers.

Alternatively one of the voxel corners can be considered instead (mustbe the same corner), e.g. the distances can be computed between top leftcorner to top left corner.

7. Sort the pairs in the list of inter_candidantes according to theirdistances, e.g. in descending order.

8. Run through the list inter_candidantes (starting from the one withlongest distance. If a valid pair (the pair is evaluated by theevaluation and refinement algorithm defined below) is found during therun, the short diameter is assigned to either this pair or to a memberof the list of intra_candidates if it exists, is valid and has a largerdistance.

If such a pair is found, the algorithm stops.

Else, the next pair in the list is evaluated.

9. If no valid pair (including intra_candidate) is found, and if therange width range_width is smaller than a given limit, increaserange_width and go to step 2. This limit can be set the double value ofthe initial range width (which is computed in step 1) for example.

Evaluation and Refinement Algorithm

The algorithm defined in this section works with the input of a pair ofvoxels. It evaluates a candidate pair, i.e. tells whether it is possibleto find inside these voxels a perpendicular axis to the long axis with adeviation angle from the direction perpendicular to the direction of thelong axis smaller than max_deviation. It also replaces the voxel centersby a pair of points within the voxel edges.

Let voxel1 be a first voxel of an input pair and voxel2 a second pointof the input pair of voxels (voxel1 and voxel2 are commutable).

For each corner point p_(i) (4 corners in total) in voxel1, if thecollinear axis to v passing through pi intersects voxel2, then the inputpair is valid and pair_(i) is defined as the diameter composed of thepoints p_(i) and the most distant intersection point with voxel2(actually only the interaction with the 4 edges are considered).Otherwise (if all axes do not intersect voxel2), go to step 3.

Center point corresponds to the projected voxel (projected as itcorresponds to the intersection between the voxel and the working plane)parallelogram geometrical center and the corner points to theparallelogram geometrical corners.

Return the pair pair_(i) (i in {1, 2, 3, 4}) having the maximum distanceas final refinement result. Stop the evaluation and refinementalgorithm.

For each corner point p_(i) in voxel1, for each corner point p_(j) invoxel2, if the deviation angle of the axis (p_(i), p_(j)) from thevector v is smaller than max_deviation, then the input pair is valid and(p_(i), p_(j)) is added to a list called candidates. Otherwise, if noaxis is found, the input pair is not valid and the algorithm stops.

Find in candidates the pair of points with the maximum distance andreplace the input pair with it.

The invention claimed is:
 1. A computer implemented method foridentifying a short axis in an image of a lesion region, the methodcomprising the steps of: inputting a set of voxels defining a 3D lesion,and defining a long axis of the lesion and a direction of a planeincluding the long axis and a short axis; dividing the long axis into aplurality of ranges, each of the plurality of ranges including a presetrange width; projecting each point of the input set of voxels onto thelong axis in a direction perpendicular or substantially perpendicular toa direction of the long axis; forming clusters of points projected ontoa same range and, within each of the formed clusters, defining a mostdistant point pair; selecting the most distant pair among the formedclusters as intra_candidate; for each of the plurality of ranges,finding inter_candidates by evaluating pairs of points with one pointbelonging to a first range and another point belonging to an adjacentrange and selecting the most distant pair of the pairs of points foreach of the plurality of ranges; selecting among the inter_candidates amost distant pair pair_inter satisfying a condition that through itsvoxels an axis is able to be drawn that is perpendicular orsubstantially perpendicular to the long axis with an angle of deviationfrom the direction perpendicular or substantially perpendicular to thelong axis that is smaller than a pre-defined value; assigning the shortaxis either to the intra_candidate or to the pair_inter if the shortaxis through its points is longer than an axis assigned to theinter_candidate; and if no pair is found for which inside the voxels ofthe pair an axis is able to be drawn that is perpendicular orsubstantially perpendicular to the long axis, increasing the presetrange width and repeating the method from the dividing step.
 2. Themethod according to claim 1, wherein if a valid pair is found, voxelcenters are replaced by edge points such that a pair is a valid pair ifinside the pair an axis is able to be drawn that is perpendicular orsubstantially perpendicular to the long axis.
 3. A non-transitorycomputer readable medium comprising computer executable program codeadapted to carry out the steps of claim 1.